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SPACE & TIME COSTS Last.fm dataset (3897 users, 3326 tags, 2849 resources) 36.9 billion entries 11.1 million entries Computing the Frobenius-norm for EACH tag pair requires 11.1 million subtractions, squaring and additions. There are a total of 5.5 million tag pairs for 3326 tags ! The amount of computations needed would be prohibitively huge!!! 19

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The new formula depends only on core tensor and factor matrix There is no need to compute any entries of purified tensor The relatively low dimensions of and implies much fewer computations needed SHORT-CUT TO EVALUATING impractical is a matrix that can be readily computed from the core tensor 20

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OTHER RANKING METHODS Freq: Resources are ranked in descending order of # of users who annotate the resource with query tags. BOW (Bag-of-Words) : Use IR; each resource is a document and each tag is a word. FolkRank [Hotho et al. 2006]: A modified version of PageRank. It follows the assumption that votes cast by important users with important tags would make the annotated resources important. 23

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OTHER RANKING METHODS LSI: This method projects the third-order tensor onto a 2D tag-resource matrix, and then applies traditional LSI on the tag-resource matrix using SVD. CubeSim: This method is similar to CubeLSI except that it computes the distance between two tags and directly from the original tensor by 24

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RANKING QUALITY Evaluation Metric Normalized Discounted Cumulative Gain (NDCG) NDCG rewards more heavily to relevant resources that are top-ranked than those that appear lower down in the list. where denotes that the metric is evaluated only on the resources that are ranked top in the list, is the relevance level of the resource ranked in the list, and is a normalization factor that is chosen so that the optimal ranking’s NDCG score is users, each proposing 8 queries 25

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RELATED WORK Matrix Factorization Our work differs from MF in two ways: We aim at capturing semantic relations among tags. We deal with a three-dimensional tensor. Hotho et al Our work differs from FolkRank in that our approach performs offline semantic analysis, which allows online query processing to be efficiently done. Wu et al Our approach is technically different from that work. Bi et al Our approach scales to large social tagging databases, which the previous work is unable to handle. 30

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CONCLUSIONS We introduce a novel tag-based framework for searching resources in social tagging systems. We study the role of taggers in search quality for social tagging systems. We propose CubeLSI, which is a 3D extension of LSI, for semantic analysis over the third-order tensor of resources, taggers, and tags. We present a comprehensive empirical evaluation of CubeLSI against a number of ranking methods on real datasets. 31